CN102547694A - Chinese-remainder-theorem-based group key creation method for sensor network - Google Patents

Abstract

The invention relates to a method for establishing a group key based on the Chinese remainder theorem in a sensor network. The pre-distribution method is adopted, and secret information is preset before the sensor nodes are spread in a specific area, and then the group key is calculated using the secret information ; When a new node joins or an old node withdraws, the group key can also be updated, which ensures the security of the network. In addition, its ability to resist attacks and cryptanalysis is stronger than the general key management scheme based on symmetric mechanism. The key management mechanism of the sensor network based on the nature of the public key is conducive to the expansion and use of the public key algorithm in its upper network (such as the transport layer and application layer network in the Internet of Things).

Description

A Group Key Establishment Method Based on Chinese Remainder Theorem in Sensor Networks

technical field

The invention relates to a sensor network security technology, in particular to a group key establishment method based on the Chinese remainder theorem in the sensor network.

Background technique

In wireless sensor networks, in order to ensure information security, communication between nodes often needs to be protected by security measures. In all security mechanisms, encryption technology is the foundation, through which security requirements such as sensor network authentication, confidentiality, non-repudiation, and integrity can be realized. For encryption technology, encryption mainly has two main components, namely algorithm and key. After years of research and development, the encryption algorithm has a very mature international standard, such as: DES, AES, etc., we can choose according to the specific application of the sensor network. But no matter how strong the encryption algorithm is, we need to negotiate the key first when conducting secret communication. If a weak key generation method is used, then the entire system is weak and there is no need to decipher the encryption algorithm. Therefore, using a strong key generation algorithm is the premise of a strong system, which is key management. Therefore, key management in sensor networks becomes a key factor affecting network security. the

According to the tracking and analysis of domestic and foreign research literature, in recent years, scholars at home and abroad have proposed a variety of key management protocols for wireless sensor networks. However, most protocols focus on the performance of the key's connectivity, invulnerability, and validity. When the sensor network is connected to the Internet of Things as the perception layer, the security of information in the network will be attacked and interfered by various types of terminals. To ensure the security of information, the key in the sensor network will need to improve its anti-attack ability or scalability.

Existing key management schemes, they all focus on key management and research based on symmetric properties. Although these key management schemes can also play a role in keeping secrets to a certain extent. But its anti-attack ability is not very strong; and once it is extended and applied to the Internet of Things, its part based on symmetric key management may become the weakness of the entire network attack.

Contents of the invention

The present invention aims at the problem of weak anti-attack ability of the key management of wireless sensor network communication nodes, and proposes a group key establishment method based on the Chinese remainder theorem in the sensor network, which is constructed by combining secret sharing and the Chinese remainder theorem Group key management scheme. Its ability to resist attacks and cryptanalysis has been enhanced. This method is based on the public key nature of the sensor network key management mechanism. Expand and use.

The technical solution of the present invention is: a method for establishing a group key based on the Chinese remainder theorem in a sensor network, and the specific steps of the method are as follows:

1) Suppose there is a base station node BS and n general nodes in the network, Gc=(N ₁ ,N ₂ ,..., N _n ) is the initial set of n general nodes;

2) The process of secret information generation and node initialization is:

Step 1: BS selects n pairs of mutually prime integers q ₁ , q ₂ , ..., q _n , and lets them serve as the private information of n nodes. Here, when i j when gcd(q _i ,q _j )=1 ; then BS randomly selects a first-degree polynomial f(x)=a ₁ x+a ₀ , let K _g be the group key, and use it as the constant term of the first-degree polynomial, That is, a ₀ =K _g ; BS randomly generates two integers as the input of f(x), and obtains two secret shares S ₀ and S _g , and S _g is used to shield the group key K _g ;

Step 2: BS uses S _g and q _i (i=1,...,n) to generate the following n sub-secrets:

BS calculates P and P _i from P= q ₁ q ₂ ... q _n , P _i = P/q _i (i=1,...,n);

At the same time, it also needs to calculate P _{i '} (i=1,...,n) from P _i P i '=1 mod _q i;

Further BS calculates y _i =c _i P _i P _i ' and s _i =y _i P;

； Step 3: BS broadcasts the message {s ₁ ,…,s _n , P ₁ ,…,P _n ,S ₀ } to all nodes in the network. If there is a key pair between BS and each node, it can also use The key pair of each node N _i secretly transmits the broadcast message, such as:

;

3) The recovery process of the group key:

When each node receives the message sent by the base station BS, the node N _i will use the private information q _i of its own node to calculate P=P _i q _i ;

Then restore y _i according to y _i =s _i /P;

计算出S _g； then by

Calculate S _g ;

Then according to the received S ₀ and the calculated S _g , the node N _i will calculate according to Shamir's secret sharing theorem

, 这里L _i (0) 是由拉格朗日插值定理计算出的系 Group-out key K _g , that is, a ₀ =

, where L _i (0) is the system calculated by the Lagrange interpolation theorem

； number

;

4) Joining of new nodes:

When a new node joins, the base station will regenerate n+1 sub-secrets from the second step of step 2); then calculate P, P _i , P _i ' , y _i , s _i ( i=1,...,n,n+1), and broadcast to all nodes; the node restores the group key in the way of step 3);

5) Revocation of nodes:

When a node needs to be withdrawn from the network, the base station will regenerate n-1 sub-secrets from the second step of step 2); then calculate P, P _i , P _i ' , y _i , s _i (i=1,...,n-1), and send it to all nodes in the way that the node encrypts the key; the node restores the group key in the way of step 3).

The beneficial effect of the present invention is that: a group key establishment method based on the Chinese remainder theorem in the sensor network of the present invention adopts a pre-distribution method, and the secret information is preset before the sensor nodes are spread in a specific area, and then the secret information is used to The information calculates the group key; when a new node joins or an old node withdraws, the group key can also be updated, which ensures the security of the network. In addition, its ability to resist attacks and cryptanalysis is stronger than the general key management scheme based on symmetric mechanism. The key management mechanism of the sensor network based on the nature of the public key is conducive to the expansion and use of the public key algorithm in its upper network (such as the transport layer and application layer network in the Internet of Things).

Detailed ways

j时gcd(q _i ,q _j )=1。假定k ₁ ,…,k _m  是m 个任意的整数。考虑如下的同余方程组: Chinese Remainder Theorem: If it is assumed that q ₁ ,...,q m _are positive integers that are mutually prime to each other, that is, when i

When j, gcd(q _i ,q _j )= 1. It is assumed that k ₁ ,...,k _m are m arbitrary integers. Consider the following congruence equations:

k ₁  mod q ₁ x

k ₁ mod q ₁

k ₂  mod q ₂ x

k ₂ mod q ₂

k _m  mod q _m x

k _m mod q _m

；而可由

得，它就是唯一解。

是的逆；

。 The unique solution of this system of equations modulo M can be obtained by the Chinese remainder theorem. here ;

; and by

Yes, it is the only solution.

yes inverse of

.

In order to provide a self-healing negotiable revocable head node and common node key distribution method, a group key establishment method based on the Chinese remainder theorem in the sensor network of the present invention is as follows:

First: In order not to lose generality, we assume that there is a base station node BS and n general nodes in the network. Gc=(N ₁ ,N ₂ ,. .., N _n ) is the initial set of n general nodes, Gc=(N ₁ ,N ₂ ,. .., N _n ).

1) The process of secret information generation and node initialization is:

Step 1: BS selects n pairwise mutually prime integers q ₁ , q ₂ , ..., q _n , and lets them be the private information of n nodes. here when i When j, gcd(q _i ,q _j )=1 . Then the BS randomly selects a first-degree polynomial f(x)=a ₁ x+a ₀ , sets K _g as the group key, and uses it as a constant term of the first-degree polynomial, that is, a ₀ =K _g . BS randomly generates two integers as the input of f(x), and obtains two secret shares S ₀ and S _g , and S _g is used to shield the group key K _g .

Step 2: BS uses S _g and q _i (i=1,...,n) to generate the following n sub-secrets:

BS calculates P and P _i from P= q ₁ q ₂ ... q _n , P _i = P/q _i (i=1,...,n);

At the same time, it also needs to calculate P _{i '} (i=1,...,n) from P _i P i '=1 mod q _i ;

Further _, BS calculates y _i =ci P _i P _i ' and s _i =y _i P.

。 Step 3: BS broadcasts the message {s ₁ ,…,s _n , P ₁ ,…,P _n ,S ₀ } to all nodes in the network. If there is a key pair between BS and each node, it can also use The key pair of each node N _i secretly transmits the broadcast message, such as:

.

2) The recovery process of the group key:

When each node receives the message sent by the base station BS, the node N _i will use the private information q _i of its own node to calculate P=P _i q _i ;

Then restore y _i according to y _i =s _i /P;

计算出S _g； then by

Calculate S _g ;

, 这里L _i (0) 是由拉格朗日插值定理计算出的系数。 Then according to the received S ₀ and the calculated S _g , the node N _i will calculate the group key K _g according to Shamir's secret sharing theorem, that is, a ₀ =

, where L _i (0) is the coefficient calculated by the Lagrange interpolation theorem .

3) Joining of new nodes:

When a new node joins, the base station will regenerate n+1 sub-secrets from the second step of the 1) process; then calculate P, P _i , P _i ' , y _i , s _i ( i=1,...,n,n+1), and broadcast to all nodes; the node restores the group key in the way of 2) process.

4) Withdrawal of nodes:

When a node needs to be withdrawn from the network, the base station will regenerate n-1 sub-secrets from the second step of the 1) process; then calculate P, P _i , P _i ' , y _i , s _i (i=1,...,n-1), and send it to all nodes in the way that the node encrypts the key; the node restores the group key in the way of 2) process.

Claims (1)

1. In the sensor network based on the group key method for building up of Chinese remainder theorem, it is characterized in that the method concrete steps are following:

   1) supposes to exist in the network base-station node BS and n general node, Gc=(N ₁, N ₂. .., N _n) be the initial sets of n general node;

   2) process of the generation of secret information and node initializing is:

   The first step: BS selects n coprime in twos integer q ₁, q ₂..., q _n, let them as the private information of n node,, work as i here

   

   During j Gcd (q _i , q _j )=1BS selects a polynomial f (x)=a at random then ₁X+a ₀, make K _gBe group key, and with it as once polynomial constant term, i.e. a ₀=K _gBS produces the input of two integers as f (x) at random, obtains two secret sharing S ₀And S _g, S _gBe to be used for the shield group key K _g;

   Second step: BS uses S _gAnd q _i(i=1 ..., n) produce n following son secret:

   BS is again by P=q ₁q ₂... q _n, P _i=P/q _i(i=1 ..., n) calculate PWith P _i

   It also will be by P simultaneously _iP _i'=1 mod q _iCalculate P _i' (i=1 ..., n);

   Further BS calculates y again _i=c _iP _iP _i' and s _i=y _iP;

   The 3rd step: BS is with message { s ₁..., s _n, P ₁..., P _n, S ₀Be broadcast to nodes all in the network, if between BS and each node pair key K is arranged _In, it also can use each node N _iKey is carried out secret transmission to broadcast, as:

   

   3) recovery process of group key:

   After each node receives the message that base station BS sends, node N _iTo use the private information q of own node earlier _iCalculate P=P _iq _i

   Again according to y _i=s _i/ P recovers y _i

   Then by

   

   Calculate S _g

   Basis receives again S ₀ With calculate S _g , node N _iTo calculate according to the secret sharing theorem of Shamir

   Go out group key K _g, promptly a ₀ =

   

   , here L _i (0)Be to be by what the Lagrange's interpolation theorem calculated

   Number

   

   ;

   4) adding of new node:

   Add fashionablely as a new node, the base station will be from step 2) second step beginning of process produces n+1 son secret again; Calculate P, P then in the same way _i, P _i', y _i, s _i(i=1 ..., n n+1), and is broadcast to all nodes; Node is again with the mode recovering group key in the step 3) process;

   5) cancelling of node:

   When a node need be cancelled from network, the base station will be from step 2) second step beginning of process produces n-1 son secret again; Calculate P, P then in the same way _i, P _i', y _i, s _i(i=1 ..., n-1), and the mode of secret key encryption is sent to all nodes with node; Node is again with the mode recovering group key in the step 3) process.